Robert Connelly

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Robert Connelly (born July 15, 1942 in Pennsylvania ) is an American mathematician who studies discrete geometry and combinatorics .

Connelly studied at the Carnegie Institute of Technology (Bachelor's degree in 1964) and received her doctorate in 1969 with James M. Kister at the University of Michigan ( Unknotting Close Embeddings of Polyhedra in Codimension Greater Than Three ). Since 1969 he has been a professor at Cornell University . He was visiting scholar at IHES , Syracuse University, Budapest, Dijon, Montreal, Bielefeld (as recipient of the Humboldt Research Award ), the University of Calgary, the University of Washington in Seattle and the University of Cambridge .

In 1977, Connelly gave the first example of a flexible polyhedron that can be converted into a second shape without self-intersection, with the side surfaces remaining rigid. According to Cauchy , such a polyhedron must be non-convex. Examples with self-overlapping were already known (Octahedron by Raoul Bricard 1897). Connelly's flexible polyhedron had 18 triangle sides, later simpler flexible polyhedra were found (for example by Klaus Steffen ). When transforming each flexible polyhedron, its volume is retained. Connelly proved this theorem (Bellow's conjecture) in 1997 with IK Sabitov and Anke Walz (for three dimensions).

Connelly broke in 2003 together with Erik Demaine and Günter Rote, the Carpenter's Rule Problem (German: folding problem ). The question is whether it is always possible to develop a rigid polygon chain without intersections continuously into a straight line. During this movement, all of the lines must keep their length and no lines may intersect. Connelly, Demaine and Rote answered this question positively.

Connelly also studies the geometry of Buckminster Fuller's tensegrity structures.

In 2012 Connelly became a Fellow of the American Mathematical Society .

The asteroid (4816) Connelly was named after him.

Fonts

  • A flexible sphere , Mathematical Intelligencer , Vol. 1, 1978, pp. 130-131
  • The Rigidity of Polyhedral Surfaces , Mathematics Magazine, Volume 52, 1979, pp. 275-283
  • Rigidity , in Handbook of Convex Geometry , Volume A, North-Holland, Amsterdam, 1993, pp. 223-271
  • with K. Bezdek Pushing disks apart - the Kneser-Poulsen conjecture in the plane , J. Reine Angew. Math., Vol. 553, 2002, pp. 221-236.
  • Generic global rigidity , discrete comput. Geom., Volume 33, 2005, pp. 549-563

Web links

Individual evidence

  1. ^ Date of birth according to Fuchs, Tabachnikov Schaubild der Mathematik , Springer Verlag 2011
  2. ^ Mathematics Genealogy Project
  3. ↑ Weisstein Flexible Polyhedron at Mathworld
  4. ↑ Robert Connelly, I. Sabitov, Anke Walz: The bellows conjecture . In: Contributions to algebra and geometry. Contributions to Algebra and Geometry . 38, No. 1, 1997, ISSN  0138-4821 , pp. 1-10.  ( Page no longer available , search in web archives )  Info: The link was automatically marked as defective. Please check the link according to the instructions and then remove this notice.@1@ 2Template: Dead Link / www.mat.ub.es  
  5. ↑ Another proof was previously given by I. Kh. Sabitov 1996, Volume of a polyhedron as a function of its metric, Fundamenti i Prikl. Mat., Vol. 2, 1996, pp. 1235-1246. See Gaidullin, Flexible polyhedra and their volumes , ECM 2016
  6. ↑ Robert Connelly; Erik Demaine; Rote, Günter: Straightening polygonal arcs and convexifying polygonal cycles . In: Discrete and Computational Geometry . 30, No. 2, 2003, pp. 205-239. Preliminary version appeared at 41st Annual Symposium on Foundations of Computer Science, 2000. doi : 10.1007 / s00454-003-0006-7 .
  7. ^ Lecture by Connelly Why things don´t fall down 2006
personal data
SURNAME Connelly, Robert
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH July 15, 1942
PLACE OF BIRTH Pennsylvania